Out of the blue: how Green Moon stopped the nation

Out of the blue Melbourne Cup winner Green Moon stormed home for victory. But the win was more than just luck, explains Stephen Holden.

The Melbourne Cup stops a nation. But that's not so hard because statistics, it must be said, can do much the same.

Of course, the Melbourne Cup is a turn-on, statistics is a turn-off.

But really, understanding statistics is as easy as interpreting the results of a horse race.

Before we all stopped to watch 'the' race on Tuesday, bookmakers and totaliser agency boards posted their odds for each horse.

Strictly, the odds offered to the public do not represent the true probabilities. They include an 'over-round' which is the margin that allows bookmakers and TABs to make a profit.

For simplicity's sake, let us just take assume that the odds do represent the probabilities of a particular horse winning the race.

The eventual winner, Green Moon, had odds posted at the TAB of 22 to 1.What does this mean?

It means (roughly) that Green Moon had a chance of less than 1 in 22 of winning the race.

In fact, with odds of greater than 20 to 1, we would therefore say that Green Moon's probability of winning the race was estimated to be less than 5 per cent.

That is, 'p' was less than .05!

Yes, this is important. This is the level at which most social science reports a "statistically significant result".

This is the level at which the social scientist - in the horribly convoluted language of statisticians - "rejects the null hypothesis that chance is operating".

There are two facts, and we are required to interpret them together.

The first fact is that Green Moon was unlikely to win at least by a social scientist's standard of p<.05.

The second fact is that Green Moon won.

Most of us probably think that the improbable happened - and if we happened to bet on Green Moon, we are ecstatic. We will be paid over $20 for each $1 we bet.

This first interpretation is that Green Moon was 'lucky' on the day. The other interpretation is to say we were surprised that the improbable event happened, and to express scepticism about whether this was a 'lucky' outcome.

If social scientists who were track-side were faithful to the p<.05 level, then when Green Moon won, they would have been contacting track stewards questioning the result. This was not chance, it was something else.

The specifics of the alternative explanations to why Green Moon won we can leave to horse racing experts, but in short, a social scientist might conclude that the race was rigged or that Green Moon 'cheated' or some other alternative hypothesis.

In statistical testing, it is not true to say that "If a p-value is less than .05, the findings are said to be statistically significant - meaning there is less than a 5 per cent chance that the results were the result of chance" as these authors recently said.

No, no, no!

The p-value is a conditional probability. It is the probability of Green Moon winning the Melbourne Cup assuming that everything is operating as it should. If we assume that everything was operating as it should, the 'p-value' represents the probability of the social scientist of making a 'false alarm', of interpreting the result as showing that something was shonky when it was not.

If the race had been won by Unusual Suspect with odds of greater than 150 to 1, Australia would probably still be excited about the win. And most of the noise would be about the legitimacy of the result.

So we cannot criticise statisticians for their logic - it is the same as ours.

When is an improbable event just an improbable event; when is it out of the ordinary, but not extraordinary like a blue moon - or a Green Moon winning the Melbourne Cup.

And when is an improbable event evidence that something else is going on? The event is so surprising that we doubt our underlying belief about how things are operating.

The question is where do we draw the line?

Stephen Holden is associate professor of marketing at Bond University. View his full profile here.